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find the equation to the locus of a point which moves so that its distance from the axis of X is always one half its distance from the origin

find the equation to the locus of a point which moves so that its distance from the axis of X is always one half its distance from the origin

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Dear Kamal
 
Let the point = (x, y)
Hence its distance from X -axis = y
 
Now
Its distance from origin = \sqrt(x² +y²)
 
Hence
(1/2)\sqrtx²+y² = y
On squaring
(1/4)(x² +y²) = y²
x² = 3y²
 
Regards
Arun (askIITians forum expert)

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